A059444 - OEIS

%I #29 Nov 27 2024 11:54:03

%S 2,0,6,6,3,6,5,6,7,7,0,6,1,2,4,6,4,6,9,2,3,4,6,9,5,9,4,2,1,4,9,9,2,6,

%T 3,2,4,7,2,2,7,6,0,9,5,8,4,9,5,6,5,4,2,2,5,7,7,8,3,2,5,6,2,6,8,9,8,9,

%U 7,8,9,6,4,2,5,6,7,0,8,5,1,6,1,8,1,2,6,0,1,8,1,2,2,7,7,3,3,1,4,1

%N Decimal expansion of square root of (Pi * e / 2).

%C Appears as constant factor in Proposition 1.12, p. 5, of Feige et al. (2007). - _Jonathan Vos Post_, Jun 18 2007

%D C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," Oxford University Press, Oxford and NY, 2001, page 68.

%H Harry J. Smith, <a href="/A059444/b059444.txt">Table of n, a(n) for n = 1..20000</a>

%H C. A. Pickover, "Wonders of Numbers, Adventures in Mathematics, Mind and Meaning," <a href="http://www.zentralblatt-math.org/zmath/en/search/?q=an:0983.00008&amp;format=complete">Zentralblatt review</a>

%H Uri Feige, Guy Kindler, Ryan O Donnell, <a href="http://eccc.hpi-web.de/eccc-reports/2007/TR07-043/Paper.pdf">Understanding Parallel Repetition Requires Understanding Foams</a>, Electronic Colloquium on Computational Complexity, Report TR07-043 (ISSN 1433-8092, 14th Year, 43rd Report), 7 May 2007.

%H OEIS Wiki, <a href="/wiki/A_remarkable_formula_of_Ramanujan">A remarkable formula of Ramanujan</a>

%F Sqrt(Pi*e/2) = A + B with A = 1 + 1/(1*3) + 1/(1*3*5) + 1/(1*3*5*7) + 1/(1*3*5*7*9) + ... = 1.410686134... (see A060196) and B = 1/(1 + 1/(1 + 2/(1 + 3/(1 + 4/(1 + 5/(1 + ...)))))) = 0.65567954241... (see A108088) - (S. Ramanujan)

%F Equals (sqrt(2)*exp(1/4)*(sum(n>=0, n!/(2*n)! ) - 1))/erf(1/2). - _Jean-François Alcover_, Mar 22 2013

%e 2.066365677...

%t RealDigits[N[Sqrt[ \[Pi]*\[ExponentialE]/2], 100]][[1]]

%t RealDigits[Sqrt[(Pi*E)/2],10,120][[1]] (* _Harvey P. Dale_, Nov 27 2024 *)

%o (PARI) { default(realprecision, 20080); x=sqrt(Pi*exp(1)/2); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b059444.txt", n, " ", d)); } \\ _Harry J. Smith_, Jun 27 2009

%Y Cf. A059445, A060196, A108088.

%K nonn,cons

%O 1,1

%A _Robert G. Wilson v_, Feb 01 2001

%E Edited by _Daniel Forgues_, Apr 14 2011